Question: Simplify the following expression: $ p = \dfrac{3}{10} + \dfrac{-2k - 9}{-2} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2}{-2}$ $ \dfrac{3}{10} \times \dfrac{-2}{-2} = \dfrac{-6}{-20} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-2k - 9}{-2} \times \dfrac{10}{10} = \dfrac{-20k - 90}{-20} $ Therefore $ p = \dfrac{-6}{-20} + \dfrac{-20k - 90}{-20} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-6 - 20k - 90}{-20} $ $p = \dfrac{-20k - 96}{-20}$ Simplify the expression by dividing the numerator and denominator by -4: $p = \dfrac{5k + 24}{5}$